In summary, we observe \(e^+e^-\rightarrow \pi ^{0}\pi ^{0}h_{c}\)  at \(\sqrt{s}=4.23\) , 4.26, and
4.36 GeV for the first time. The measured Born cross sections are about half of those for
\(e^+e^-\rightarrow \pi ^+\pi ^-h_c\) , and agree with expectations based on isospin symmetry within systematic uncertainties.
A narrow structure with a mass of \((4023.9\pm 2.2\pm 3.8)\)  MeV/\(c^2\)  is observed in the \(M^{\rm recoil}_{\pi ^0}|_{\rm max}\)  mass
spectrum. This structure is most likely the neutral isospin partner of the
charged \(Z_c(4020)\)  observed in the \(e^+e^-\rightarrow \pi ^{+}\pi ^{-}h_c\)  process [1]}.
This observations indicate that there is no anomalously large isospin violations in \(\pi \pi h_c\)  and \(\pi Z_c(4020)\)  system.
